Principles and psychophysics of Active Inference - Probabilities and Optimal Inference to Understand the Brain

Principles and psychophysics of Active Inference in anticipating a dynamic, switching probabilistic bias

Laurent Perrinet, Chloé Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain

* (AUTHOR) Hi, I am Laurent Perrinet from (LOGO) the Institute de Neurosciences de la Timone in Marseille, a joint unit from the CNRS and AMU. Using computational models, I am investigating the link between the efficiency of behavioural responses in vision, their underlying neural code and their adaptation to the structure of the world.

* (SHOW TITLE - THEME) = In particular, I will try to illustrate how we may use predictive mechanism to understand our capacity to anticipate in a dynamic, poissbly volatile environment

http://invibe.net/LaurentPerrinet/Presentations/2018-04-05_BCP_talk

Principles and psychophysics of Active Inference in anticipating a dynamic, switching probabilistic bias

Laurent Perrinet, Chloé Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain

Outline

Motivation

Raw psychophysical results

The Bayesian Changepoint Detector

Results using the BCP

Motivation - a Real-life example

Motivation - Eye Movements

Motivation - Random-length block design

Outline

Motivation

Raw psychophysical results

The Bayesian Changepoint Detector

Results using the BCP

Raw psychophysical results - Random-length block design

Raw psychophysical results

Raw psychophysical results - Fitting eye movements

Raw psychophysical results

Outline

Motivation

Raw psychophysical results

The Bayesian Changepoint Detector

Results using the BCP

The Bayesian Changepoint Detector

Bayesian Changepoint Detector

Initialize

$P(r_0)= S(r)$ or $P(r_0=0)=1$ and
$ν^{(0)}_1 = ν_{prior}$ and $χ^{(0)}_1 = χ_{prior}$

Observe New Datum $x_t$
Evaluate Predictive Probability $π_{1:t} = P(x |ν^{(r)}_t,χ^{(r)}_t)$
Calculate Growth Probabilities $P(r_t=r_{t-1}+1, x_{1:t}) = P(r_{t-1}, x_{1:t-1}) π^{(r)}_t (1−H(r^{(r)}_{t-1}))$
Calculate Changepoint Probabilities $P(r_t=0, x_{1:t})= \sum_{r_{t-1}} P(r_{t-1}, x_{1:t-1}) π^{(r)}_t H(r^{(r)}_{t-1})$
Calculate Evidence $P(x_{1:t}) = \sum_{r_{t-1}} P (r_t, x_{1:t})$
Determine Run Length Distribution $P (r_t | x_{1:t}) = P (r_t, x_{1:t})/P (x_{1:t}) $
Update Sufficient Statistics :

$ν^{(0)}_{t+1} = ν_{prior}$, $χ^{(0)}_{t+1} = χ_{prior}$
$ν^{(r+1)}_{t+1} = ν^{(r)}_{t} +1$, $χ^{(r+1)}_{t+1} = χ^{(r)}_{t} + u(x_t)$

Perform Prediction $P (x_{t+1} | x_{1:t}) = P (x_{t+1}|x_{1:t} , r_t) P (r_t|x_{1:t})$
go to (2)

The Bayesian Changepoint Detector

Outline

Motivation

Raw psychophysical results

The Bayesian Changepoint Detector

Results using the BCP

Results using the BCP - inference with BCP

Results using the BCP - fit with BCP

Principles and psychophysics of Active Inference in anticipating a dynamic, switching probabilistic bias

Laurent Perrinet, Chloé Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain